#### What is the measure of <w in the right-angle triangle given below? ( Plane geometry)ACT Math Practice Test

E is the best option. Since it is a right-angle triangle, therefore, angle y is equal to 90°. Since we are given the value of <z, so we can find the value of <x because <x+<y<z=180°. <x=45°. Since, we know the rule of geometry which says that sum of an exterior angle is equal to the sum of two remote interior angles. <w is an exterior angle and it is equal to <x+<z. <x and <z both are equal to 45°, so <w will be equal to 90°. A cannot be true as it reflects measure of one interior angle. B is incorrect as sum of two interior angles is not equal to 60°. Similarly, options C and D are also incorrect as they do not reflect the sum of angles x and z.

#### In the right-angle triangle given below, what is the value of y? (Plane geometry)

D is the best option. According to Pythagoras theorem, in the right-angle triangle the square of the hypotenuse length is equal to the sum of squares of other two sides.
Here, y^{2}=x^{2}+z^{2}
y^{2}= 49+81
=130
y=11.4
A is incorrect as it is the square of one side only. B is also incorrect as it is the square of side z. c is incorrect as it is the difference of the sides of the triangle. E is incorrect as it is calculated by taking the square root of the sum of difference of sides a and z.

#### If sin^{2}θ=0.75, then cos θ=?( Trigonometry)

B is the best option. We know that cos^{2} θ + sin^{2} θ = 1
cos^{2} θ=1- sin^{2} θ
=0.25
Now, taking under root of 0.25, we get 0.5 which is the value of cos θ.
A cannot be true as it is the value of cos^{2} θ. C is incorrect as cos^{2} θ + sin^{2} θ = 1. D is incorrect as it is the value for sin θ. E is also incorrect as the value given for sin^{2} θ is 0.75 not 1.

#### The total amount spent on Christmas by Sarah, Joe, Mariah and Alice was $4300. The following pie chart shows the percentage distribution of the amount spent. What is the central angle of Alice? (Plane geometry)

C is the best option. Central angle for Alice=35/100x 360 =126° A, B and D are incorrect as they do not reflect 35% spending by Alice. E cannot be true as it is the sum of the central angles of pie chart.

#### What is solution to the equation x^{2}+8x+15? (Intermediate algebra)

A is the best option. x^{2}+8x+15
= x^{2}+3x+5x+15
x(x+3)+5(x+3)=0
x=-3 or x=-5
B is incorrect as the constant will have the negative value when it is shifted on the other side of the equality. C, D and E are also incorrect as after expanding the equation we did not get these values.

#### What is the perimeter of the triangle given below? ( Plane geometry)

C is the best option. The perimeter of the triangle is calculated by the formula a+b+c. =3√3+6√3+4√5 = 9√3+4√5 A is incorrect as all the constants cannot be added together as the under roots are not same. B is incorrect as it has taken the square of √3 and multiplied it with the constants which is wrong. D is incorrect as we cannot add all the constants if they do not have the same under roots. E is also incorrect as we do not get this answer when we add all the three sides together.

#### If 25% of the given number is 12.5, then what is 60% of the same number? ( Elementary algebra)

D is the best answer. First, we will find the number. 25/100x=12.5 x = 50 Now, find 60% of 50 60/100 x 50 = 30 A is not true as it is the number. B is incorrect because it is the percentage of the number. C and e are incorrect as they do not reflect 60% of the number.

#### Consider these three integers which are added together to get the number 29. (Elementary algebra) x-3 2x+1 x-1 Find the value of x.

A is the best answer. x-3+2x+1+x-1=29 4x-3=29 4x=32 x=8. B, C, D and E cannot be true as they do not reflect the value of x.

#### Line A is perpendicular to the line B -1/3 x+7. What is slope of the line A?( Coordinate geometry)

D is the best answer. Slope of two perpendicular lines are negative reciprocals of each other. Slope of line B = -1/3 Slope of line A=3 A cannot be true as it is the value of b for the line B. B is incorrect as it is the slope of the line B. C is incorrect as it has changed the sign but the reciprocal is not taken. E is incorrect as slope should negative reciprocal of -1/3.

#### John bought a car on lease and paid $2000 initially. He will also pay $450 every month. Which of the following expression can be used to calculate the total amount that John will pay for the car? (Elementary algebra)

C is the best option. Initial amount = $2000 Amount paid in x months= 450x Total amount=2000+450x A and D answers are not true as the variable x cannot be written with the initial amount. B and E cannot be true as the variable amount i.e. amount paid each month will be added in the initial amount $2000.

#### Identify the mode in the following sequence. (Pre-algebra) 2,11,5,7,6,7,11,5,11,6

C is the best answer. Mode is the most repeated value. Since, 11 is repeated 3 times and it is the most repeated value, therefore, it is the mode. Options A and B are incorrect because 5 and 7 are repeated 2 times only. D is incorrect because 4 is not present in the sequence. E is incorrect because it is the mean of the sequence not the mode.

#### The inequality -7x+9>37 is equal to: (Intermediate algebra)

E is the best option. We will solve the inequality like this: -7x+9>37 -7x>28 We will divide both sides by -7, so the inequality sign will be also reversed. x28 after subtracting 9 from 37.

#### Solve for x: 8^{x-2}=64(Intermediate algebra)

C is the best answer. Both 8 and 64 can be written as exponents with base 2.
2^{3(x-2)}=2^{6}
3(x-2)=6
3x-6=6
3x=12
x=4
A is incorrect as 3x=12 not x=12. B, D and E are incorrect because we do not get these answers when we solve for x.

#### If a=x+4, b=3,y=-2 and c=5, then simplify the polynomial a^{2}b^{2}-2y+3c. (elementary algebra)

D is the best option. Put the given values in the polynomial.
=(x+4)^{2}(3)^{2}-2(-2)+3(5)
=(x+4)^{2}9 +4+15
=(x+4)^{2}9+19
Expand (x+4)^{2}using FOIL method
=(x^{2}+4x+4x+16)9+19
=(x^{2}+8x+16)9+19
=9x^{2}+72x+144+19
=9x^{2}+72x+163
A is incorrect because it has not added 19 after expanding the equation. B is incorrect because 72x contains positive rather than the negative sign. C is incorrect because the expression (x+4)2 will be multiplies by 9. E is incorrect because +19 is missing from the expression.

#### |-13| is equal to (Intermediate algebra)

A is the best option. The digit inside the symbols || is refereed as absolute value and it is equal to the number itself regardless of its sign. B is incorrect because absolute value of a negative number is also the positive number. C, D and E cannot be true as they do not reflect the absolute value of |-13|.