# SAT ACT Common Core State Standard Math Practice Test Question AMBQID PDF

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## SAT Math Practice Test Sample Questions AMQID 101 to 110

**SAT Math Practice Test**: **AMBQID 101**

In the given figure, the quadrilateral is a rectangle and both red regions have equal area. Find cosθ.

**Math Problems to Solve AMBQID 101 Solution :**

**SAT Math Practice Test**: **AMBQID 102**

If the product of first 20 prime numbers is divided by 4, then find remainder.

**Math Problems to Solve AMBQID 102 Solution :**

**SAT Math Practice Test**: **AMBQID 103**

If a = 11111…1(55 digits), b = 1 + 10 + 10^{2} + 10^{3} + 10^{4}, c = 1 + 10^{5} + 10^{10} + 10^{15} + … + 10^{50}, then, which one is correct?

**Math Problems to Solve AMBQID 103 Solution :**

**SAT Math Practice Test**: **AMBQID 104**

In triangle ABC, the median through A is perpendicular to AB, then

**Math Problems to Solve AMBQID 104 Solution :**

**SAT Math Practice Test**: **AMBQID 105**

In the given figure, find the number of parallelograms.

**Math Problems to Solve AMBQID 105 Solution :**

**SAT Math Practice Test**: **AMBQID 106**

Find the slope of line with a positive rational slope, which passes through (6, 0) and at a distance of 5 from (1, 3).

**Math Problems to Solve AMBQID 106 Solution :**

**SAT Math Practice Test**: **AMBQID 107**

If x >= y and y > 1 , then which one cannot be the value of log_{x}(x/y) + log_{y}(y/x).

**Math Problems to Solve AMBQID 107 Solution :**

**SAT Math Practice Test**: **AMBQID 108**

If the equation 2x^{2} – (N^{3} + 8N – 1)x + (N^{2} – 4N) = 0 has roots of opposite sign. Then the value of N cannot be equal to

**Math Problems to Solve AMBQID 108 Solution :**

**SAT Math Practice Test**: **AMBQID 109**

If x = 33^{n}, n is a positive integral. Find the probability that x has 3 in unit place.

**Math Problems to Solve AMBQID 109 Solution :**

**SAT Math Practice Test**: **AMBQID 110**

Find the derivative of log_{e}|x|.

**Math Problems to Solve AMBQID 110 Solution :**

## SAT Math Sample Questions AMQID 111 to 120

**SAT Math Sample Questions**: **AMBQID 111**

If area of circle = 30 and area of the triangle = 15, then find the value of sinα + sinβ + sin????.

**Math Problems to Solve AMBQID 111 Solution :**

**SAT Math Sample Questions**: **AMBQID 112**

P(N) = product of digits of N and S(N) = Sum of Digits of N. If N is a two-digits number such that N = P(N) + S(N). Find the number of values of N.

**Math Problems to Solve AMBQID 112 Solution :**

**SAT Math Sample Questions**: **AMBQID 113**

If x = b + c – 2a, y = c + a – 2b, z = a + b – 2c, then find the value of x^{2} + y^{2} – z^{2} + 2xy.

**Math Problems to Solve AMBQID 113 Solution :**

**SAT Math Sample Questions**: **AMBQID 114**

Find the value of cotθ/2 in the figure below.

**Math Problems to Solve AMBQID 114 Solution :**

**SAT Math Sample Questions**: **AMBQID 115**

If n! has four zeroes at the end and (n+1)! has six zeroes at the end. Find the value of n.

**Math Problems to Solve AMBQID 115 Solution :**

**SAT Math Sample Questions**: **AMBQID 116**

In the given figure, find the value of (a + b).

**Math Problems to Solve AMBQID 116 Solution :**

**SAT Math Sample Questions**: **AMBQID 117**

If N = log_{2}5^log_{5}2^log_{2}7^log_{7}5^log_{5}8, then find the value of N.

**Math Problems to Solve AMBQID 117 Solution :**

**SAT Math Sample Questions**: **AMBQID 118**

If f(x) = x/(x + 1), then find the value of f(1/13) + f(2/12) + f(3/11) + f(4/10) + …f(12/1) + f(13/1) = p/q, where HCF(p, q) = 1, then find the value of (p – q).

**Math Problems to Solve AMBQID 118 Solution :**

**SAT Math Sample Questions**: **AMBQID 119**

Two squares are chosen at random on a chessboard. Find the probability that they have a common side.

**Math Problems to Solve AMBQID 119 Solution :**

**SAT Math Sample Questions**: **AMBQID 120**

Find the limit (x tends to infinity).

**Math Problems to Solve AMBQID 120 Solution :**

## SAT Math Topics Questions AMQID 121 to 130

**SAT Math Topics Question**: **AMBQID 121**

O_{1} and O_{2} are centres of circles. PQ = 8 and QS = 18. Find AQ.

**Math Problems to Solve AMBQID 121 Solution :**

**SAT Math Topics Question**: **AMBQID 122**

4^{2n} + 4^{2n+1} has 42 divisors. Find n

**Math Problems to Solve AMBQID 122 Solution :**

**SAT Math Topics Question**: **AMBQID 123**

If x^{4} + 1/x^{4} = 527, then find the value of (x – 1)(x – 2)(x – 3)(x – 4).

**Math Problems to Solve AMBQID 123 Solution :**

**SAT Math Topics Question**: **AMBQID 124**

In the given figure, find the value of (a.tanα.sinθ)/(bcosβ).

**Math Problems to Solve AMBQID 124 Solution :**

**SAT Math Topics Question**: **AMBQID 125**

In the given figure, find the area of square.

**Math Problems to Solve AMBQID 125 Solution :**

**SAT Math Topics Question**: **AMBQID 126**

Find the slope of GC.

**Math Problems to Solve AMBQID 126 Solution :**

**SAT Math Topics Question**: **AMBQID 127**

Find the value of the logarithmic expression as below.

**Math Problems to Solve AMBQID 127 Solution :**

**SAT Math Topics Question**: **AMBQID 128**

Find the sign of a, b, c and D.

**Math Problems to Solve AMBQID 128 Solution :**

**SAT Math Topics Question**: **AMBQID 129**

If (a^{3} – 1)x^{2} + (a + b – 1)x + (a + b + c) = 0 has three roots, then find the value of (a – b – c).

**Math Problems to Solve AMBQID 129 Solution :**

**SAT Math Topics Question**: **AMBQID 130**

Find the value of (m^{9} – 9m^{3}n^{3} – n^{9}).

**Math Problems to Solve AMBQID 130 Solution :**

## SAT Math Sections Questions AMBQID 131 to 140

**SAT Math Sections Question**: **AMBQID 131**

In an isosceles triangle, if perimeter > 3(Length of Base). Find the smallest integral value of largest internal angle.

**Math Problems to Solve AMBQID 131 Solution :**

**SAT Math Sections Question**: **AMBQID 132**

If sum of five different positive integers = 106. Find maximum positive integer among five integers.

**Math Problems to Solve AMBQID 132 Solution :**

**SAT Math Sections Question**: **AMBQID 133**

Find the angle x.

**Math Problems to Solve AMBQID 133 Solution :**

**SAT Math Sections Question**: **AMBQID 134**

If π/2 < α < β < π, which of the following is FALSE?

**Math Problems to Solve AMBQID 134 Solution :**

**SAT Math Sections Question**: **AMBQID 135**

Find the value of (x + y).

**Math Problems to Solve AMBQID 135 Solution :**

**SAT Math Sections Question**: **AMBQID 136**

Find the value of (cot α – cot ????)/cot β.

**Math Problems to Solve AMBQID 136 Solution :**

**SAT Math Sections Question**: **AMBQID 137**

Find the limit (x tends to infinity).

**Math Problems to Solve AMBQID 137 Solution :**

**SAT Math Sections Question**: **AMBQID 138**

If α and β are roots of 2x^{2} – 35x + 2 = 0. Find value of (2α – 35)^{3}(2β – 35)^{3}.

**Math Problems to Solve AMBQID 138 Solution :**

**SAT Math Sections Question**: **AMBQID 139**

Find perimeter of obtuse angled triangle whose sides are consecutive integers.

**Math Problems to Solve AMBQID 139 Solution :**

**SAT Math Sections Question**: **AMBQID 140**

If x + y = 1050, then find maximum HCF of x and y.

**Math Problems to Solve AMBQID 140 Solution :**

## ACT Math Practice Test Questions AMBQID 141 to 150

**ACT Math Practice Test Question**: **AMBQID 141**

Find x in the given figure below.

**Math Problems to Solve AMBQID 141 Solution :**

**ACT Math Practice Test Question**: **AMBQID 142**

Find the unit digit of the given expression.

**Math Problems to Solve AMBQID 142 Solution :**

**ACT Math Practice Test Question**: **AMBQID 143**

Find the value of the given expression.

**Math Problems to Solve AMBQID 143 Solution :**

**ACT Math Practice Test Question**: **AMBQID 144**

Find BC in the figure below.

**Math Problems to Solve AMBQID 144 Solution :**

**ACT Math Practice Test Question**: **AMBQID 145**

O is center of semi-circle (radius = 12) and O’ is center of circle (radius = 4). Then, find AB.

**Math Problems to Solve AMBQID 145 Solution :**

**ACT Math Practice Test Question**: **AMBQID 146**

If (2020!)! is divisible by ((n!)!)!, then find the largest natural number n.

**Math Problems to Solve AMBQID 146 Solution :**

**ACT Math Practice Test Question**: **AMBQID 147**

If x and y are distinct number such that 2020 + x = y^{2} and 2020 + y = x^{2}, then find the product xy.

**Math Problems to Solve AMBQID 147 Solution :**

**ACT Math Practice Test Question**: **AMBQID 148**

If 3/2 < x < 5/2, then find the value of given expression.

**Math Problems to Solve AMBQID 148 Solution :**

**ACT Math Practice Test Question**: **AMBQID 149**

If N is the smallest natural number such that N = x^{3} = y^{5}, x and y are distinct integers. Find the sum of digits of N.

**Math Problems to Solve AMBQID 149 Solution :**

**ACT Math Practice Test Question**: **AMBQID 150**

A square with area 30 is divided by a diagonal and then into triangles. Find the areas of some of these triangles are given.

**Math Problems to Solve AMBQID 150 Solution :**

## ACT Math Sample Questions AMBQID 151 to 160

**ACT Math Sample Question**: **AMBQID 151**

P is in the interior of triangle ABC. Lines through P parallel to the sides of triangle ABC, then the resulting smaller triangles have areas t_{1} = 4, t_{2} = 9, t_{3} = 49. Find the area of triangle ABC.

**Math Problems to Solve AMBQID 151 Solution :**

**ACT Math Sample Question**: **AMBQID 152**

A triangle ABC have sides a, b, c such that a^{2} + b^{2} = 101c^{2}, then find cotC/(cotA + cotB).

**Math Problems to Solve AMBQID 152 Solution :**

**ACT Math Sample Question**: **AMBQID 153**

If a rectangle is divided into three smaller rectangle. Find the perimeter of shaded rectangle.

**Math Problems to Solve AMBQID 153 Solution :**

**ACT Math Sample Question**: **AMBQID 154**

In a triangle ABC with sides a, b, c such that tanA : tanB : tanC = 1 : 2 : 3, then find the value of a : b : c.

**Math Problems to Solve AMBQID 154 Solution :**

**ACT Math Sample Question**: **AMBQID 155**

Find the value of tan(Alpha) x tan(Beeta).

**Math Problems to Solve AMBQID 155 Solution :**

**ACT Math Sample Question**: **AMBQID 156**

Evaluate:

**Math Problems to Solve AMBQID 156 Solution :**

**ACT Math Sample Question**: **AMBQID 157**

ABCD is a rhombus and 2(Alpha) – Beeta = 60 degree, then find theta.

**Math Problems to Solve AMBQID 157 Solution :**

**ACT Math Sample Question**: **AMBQID 158**

If 1/3 + 13/15 + 33/35 + 61/63 + … + 397/399 = x y/z, then find x + y + z.

**Math Problems to Solve AMBQID 158 Solution :**

**ACT Math Sample Question**: **AMBQID 159**

ABCD is a rectangle and OA = OC, then find the angle APD.

**Math Problems to Solve AMBQID 159 Solution :**

**ACT Math Sample Question**: **AMBQID 160**

In the given figure below, ABCD is a rhombus. Find the angle theta.

**Math Problems to Solve AMBQID 160 Solution :**

## ACT Math Topics Questions AMBQID 161 to 170

**ACT Math Topic Question**: **AMBQID 161**

In p(x) = x3 + ax2 + bx + c, mean of its roots, product of its roots and the sum of its coefficient are equal. If y-intercept of the graph of y = p(x) is 2, then find the value of b.

**Math Problems to Solve AMBQID 161 Solution :**

**ACT Math Topic Question**: **AMBQID 162**

If AB = CD, then find the value of cot(Alpha) – tan(Beeta).

**Math Problems to Solve AMBQID 162 Solution :**

**ACT Math Topic Question**: **AMBQID 163**

In the given figure below, find the value of tan(Alpha + Beeta).

**Math Problems to Solve AMBQID 163 Solution :**

**ACT Math Topic Question**: **AMBQID 164**

Find the sum of the series.

**Math Problems to Solve AMBQID 164 Solution :**

**ACT Math Topic Question**: **AMBQID 165**

Find the value of tan(Theta).

**Math Problems to Solve AMBQID 165 Solution :**

**ACT Math Topic Question**: **AMBQID 166**

ABCD is a square, then find tan(theta).

**Math Problems to Solve AMBQID 166 Solution :**

**ACT Math Topic Question**: **AMBQID 167**

Evaluate.

**Math Problems to Solve AMBQID 167 Solution :**

**ACT Math Topic Question**: **AMBQID 168**

In the given figure below, find the perimeter of the sector AOB.

**Math Problems to Solve AMBQID 168 Solution :**

**ACT Math Topic Question**: **AMBQID 169**

In the given figure below, find the value of mn.

**Math Problems to Solve AMBQID 169 Solution :**

**ACT Math Topic Question**: **AMBQID 170**

In the given figure below, find the value of CD.

**Math Problems to Solve AMBQID 170 Solution :**

## ACT Math Sections Questions AMBQID 171 to 180

**ACT Math Section Question**: **AMBQID 171**

In the figure below, find x.

**Math Problems to Solve AMBQID 171 Solution :**

**ACT Math Section Question**: **AMBQID 172**

In the figure below, find the value of h.

**Math Problems to Solve AMBQID 172 Solution :**

**ACT Math Section Question**: **AMBQID 173**

In the figure below, find r.

**Math Problems to Solve AMBQID 173 Solution :**

**ACT Math Section Question**: **AMBQID 174**

Find OP.

**Math Problems to Solve AMBQID 174 Solution :**

**ACT Math Section Question**: **AMBQID 175**

Find AD.

**Math Problems to Solve AMBQID 175 Solution :**

**ACT Math Section Question**: **AMBQID 176**

Let a, b, c, d, e are distinct integers such that (6 – a)(6 – b)(6 – c)(6 – d)(6 – e) = 45, find the value of (a + b + c + d + e).

**Math Problems to Solve AMBQID 176 Solution :**

**ACT Math Section Question**: **AMBQID 177**

If 12(x!) + 5(x + 1)! = (x + 2)!, find the value of x.

**Math Problems to Solve AMBQID 177 Solution :**

**ACT Math Section Question**: **AMBQID 178**

Find shaded area in the figure below.

**Math Problems to Solve AMBQID 178 Solution :**

**ACT Math Section Question**: **AMBQID 179**

In the given figure below, find the value of L_{1}/L_{2}.

**Math Problems to Solve AMBQID 179 Solution :**

**ACT Math Section Question**: **AMBQID 180**

ABCD is a square of area 9 sq. unit. Q is a point of trisection of BD, then find cot(Alpha/2).

**Math Problems to Solve AMBQID 180 Solution :**

## Common Core Math State Standards Math Practice Test Questions AMBQID 181 to 190

**Common Core Math State Standards Math Practice Test**: **AMBQID 181**

If p(x) = x^{27} + 3x^{19} + 5x^{3} – 2x^{2} – 8 is divided by d(x) = x^{2} + x + 1, then the remainder r(x). Find r(1).

**Math Problems to Solve AMBQID 181 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 182**

In the figure below, find AC.

**Math Problems to Solve AMBQID 182 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 183**

In the figure below, find (b – c).

**Math Problems to Solve AMBQID 183 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 184**

If cotB = (sin A – sin C) / (cos C – cos A), then A, B, C are in

**Math Problems to Solve AMBQID 184 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 185**

If ax^{2} – bx + 5 = 0 does not have two distinct real roots, then minimum value of (5a + b) is

**Math Problems to Solve AMBQID 185 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 186**

Find ax^{5} + by^{5}.

**Math Problems to Solve AMBQID 186 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 187**

Find set of points (x, y) for which sin(X + Y) = sin X + sin Y.

**Math Problems to Solve AMBQID 187 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 188**

If A(0, -10) and B(2, 0) and C on the parabola y = x^{2}. Find minimum value of area of triangle ABC.

**Math Problems to Solve AMBQID 188 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 189**

Find number of non-negative integers solutions to the system of the given equations.

**Math Problems to Solve AMBQID 189 Solution :**

**Common Core Math State Standards Math Practice Test**: **AMBQID 190**

Find the type of the triangle ABC.

**Math Problems to Solve AMBQID 190 Solution :**

## CCSS Math Standard Questions AMBQID 191 to 200

**CCSS Math Standard Question**: **AMBQID 191**

Evaluate the expression.

**Math Problems to Solve AMBQID 191 Solution :**

**CCSS Math Standard Question**: **AMBQID 192**

If coordinate of vertices of a square ABCD is A(a, 1), B(b, 5), C(c, 11) and D(d, 7), then find the area of square ABCD.

**Math Problems to Solve AMBQID 192 Solution :**

**CCSS Math Standard Question**: **AMBQID 193**

If the sum of digits of product (8) x (8888…up to n digits) is 1000, then find n.

**Math Problems to Solve AMBQID 193 Solution :**

**CCSS Math Standard Question**: **AMBQID 194**

Find |a – b|.

**Math Problems to Solve AMBQID 194 Solution :**

**CCSS Math Standard Question**: **AMBQID 195**

Find the sum.

**Math Problems to Solve AMBQID 195 Solution :**

**CCSS Math Standard Question**: **AMBQID 196**

Find the shaded area.

**Math Problems to Solve AMBQID 196 Solution :**

**CCSS Math Standard Question**: **AMBQID 197**

Find the last digit of smallest positive integer whose the sum of digit is 2021.

**Math Problems to Solve AMBQID 197 Solution :**

**CCSS Math Standard Question**: **AMBQID 198**

Evaluate .

**Math Problems to Solve AMBQID 198 Solution :**

**CCSS Math Standard Question**: **AMBQID 199**

Find smallest three digit number ABC such that ABC = A + B + C + AB + BC + CA + ABC.

**Math Problems to Solve AMBQID 199 Solution :**

**CCSS Math Standard Question**: **AMBQID 200**

If AB = 4, then find the saded area.

**Math Problems to Solve AMBQID 200 Solution :**

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