**PSAT Math Practice Test Answers :**

Here we are going to see some practice questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

**Question 1 :**

In the figure given below, there is a function plotted and there are 5 points tabeled A through E drawn. For how many points is y(x) equal to 0 ?

**(A) 0 (B) 1 (C) 2 (D) 3 (E) undefined**

**Solution :**

y(x) = 0

The graph intersects x-axis at two points. B and E are the roots of the function.

**Question 2 :**

At what time on a clock will the hands form an acute tangle formed of 60 degree?

(A) 1 : 00 PM (B) 1 : 15 PM (C) 2 : 00 PM

(D) 2 : 30 PM (E) 3 : 00 PM

**Solution :**

For example, let us consider the picture given above. At 3 PM, it makes an angle 90 degree.

By dividing 90 into three equal parts, we will get each angle as 30 degree.

We can see that 2 : 00, 60 degree is formed between the hands 12 and 2.

**Question 3 :**

A jar contains only red and blue marbles. The probability of picking a red marble is 20% . One blue marble is added to the jar. What is the probability of picking a blue marble ?

(A) 1/3 (B) 1/2 (C) 4/5 (D) 1/6

(E) cannot be determined from the information given.

**Solution :**

Let "A" be the event of getting blue marble

p(A) = 20/100

P(A) = 1/5

The answer to this question depends on the number of blue marbles in the bag. Hence the answer is E.

**Question 4 :**

If a = 35, what is, (-6)^{2} (-6)(-6) + 6(-6) in terms of a ?

(A) a + 1 (B) a^{2} (C) a^{2} + 1 (D) a^{2} + a (E) 35a

**Solution :**

= (-6)^{2} (-6)(-6) + 6(-6)

= 36 (36) - 36

= 36^{2} - 36

= 36(36 - 1)

= 36 (35)

= (35 + 1) 35

= (a + 1)a

= a^{2} + a

**Question 5 :**

A circle and a regular octagon are having the same perimeter (circumference of the circle). If the side length of the octagon is a, the radius of the circle is r, then what is the radius in terms of the side length of the octagon ?

(A) 4a (B) a/π (C) 4/π (D) 4a/π (E) 4π

**Solution :**

The eight sided polygon is known as octagon.

Circumference of circle = Perimeter of octagon

2πr = 8a

r = 8a/2π

r = 4a/π

**Question 6 :**

What is the least integer greater than the greatest integer less than 1.5 ?

(A) 2 (B) 1.5 (C) 0.5 (D) 1 (E) 0

**Solution :**

The greatest integer less than 1.5 is 1 and least integer greater than 1 is 2. Hence the answer is 2.

**Question 7 :**

What is the area of a semicircle in terms of "t" with radius r. "t" is double the value of π

(A) t^{2} r (B) tr^{2} (C) tr/4 (D) tr/2 (E) tr^{2}/4

**Solution :**

Area of semicircle = (1/2)πr^{2}

t = 2π

π = t/2

= (1/2)(t/2)r^{2}

Area of semicircle = (tr^{2}/4)

**Question 8 :**

If F = - kx and greater than 0, then what happens to the vlaue of k if F triples in value and x remains constant.

(A) increases (B) Doubles (C) Decreases (D) Remains constant

(E) cannot be determined from the information given.

**Solution :**

If F = -kx, then either k or x must be negative. Since F is greater than 0. We do not know which is negative. So, we cannot determine a definite answer.

Hence the answer is E.

**Question 9 :**

If the length of the side of a square is 7^{a}, what is the area ?

(A) 7^{a} (B) 2 ⋅ 7^{a} (C) 49^{a} (D) 7^{2a} (E) 7a^{a}

**Solution :**

Area of square = a^{2}

Side of square = 7^{a}

= (7^{a})^{2}

= 7^{2a}

**Question 10 :**

What is the circumference of the dotted section of the circle whose center is O below ?

**(A) 6π (B) **** 12π (C) 24π (D) 48π (E) 64π**

**Solution :**

Equating two radii

3x - 12 = 2x

3x - 2x = 12

x = 12

2x = 24 = radius

The dotted section is a quadrant. That is, one fourth of the entire circle.

Perimeter of circle = 2πr

= 2π(24)

= 48π

Dividing the circumference by 4, we get 12π. Hence the answer is 12π.

**Question 11 :**

Given that 0 < x < 1, and set A = {x, x^{2}, x^{3}, x^{4}}, what is the smallest value in set A ?

(A) x (B) x^{2} (C) x^{3} (D) x^{4 }

(E) cannot be determined

**Solution :**

Let x = 0.5

x^{2} = 0.25

x^{3} = 0.125

x^{4} = 0.0625

When the power is being increased, the answer gets decreased. Hence the smallest value of the given set is x^{4}

**Question 12 :**

Sammy has a faulty clock. Every 15 degrees that one of the hands moves, 5 minutes passes. If a hand is initially 5 : 35 PM, in how long will be the hand be at that same position ?

(A) 65 minutes (B) 2 hours (C) 1 hour

(D) 45 minutes (E) 1 hour and 15 minutes

**Solution :**

There are 360 degree that the hands must move to complete a full revolution and to be at the same time of 5 :35.

360/24 = 15 degree

if every 15 degree, 5 minutes passes, then (24⋅5) minutes will have passed by the time it is 5 : 35 PM again.

This is, 2 hours.

**Question 13 :**

If (x - 2) (x + 2) = ax^{2} + bx + c, what is the sum of a, b and c ?

(A) -4 (B) -3 (C) 0 (D) 1 (E) 5

**Solution :**

ax^{2} + bx + c = (x - 2)(x + 2)

= x^{2} - 2x + 2x - 4

= x^{2} - 0x - 4

a = 1, b = 0 and c = -4

a + b + c = 1 + 0 + (-4)

a + b + c = -3

**Question 14 :**

Natalie walks in a special way. After every 2 steps she takes, she takes 1 step in the opposite direction. She starts at point A and walks forward. When she is 7 steps away from the point A, she has reached her destination point B. How many steps in total did she take to get from point A to B.

(A) 7 (B) 8 (C) 17 (D) 15 (E) 18

**Solution :**

When she takes two steps forward, she takes 1 step in the opposite direction.

From the picture given above, she has taken 3 steps.

1 |
landing in step 2 and going back to step 1 |
3 steps taken. | |

2 |
landing in step 3 and going back to step 2 |
6 steps taken. | |

3 |
landing in step 4 and going back to step 3 |
9 steps taken. | |

4 |
landing in step 5 and going back to step 4 |
12 steps taken. | |

5 |
landing in step 6 and going back to step 5 |
15 steps taken. | |

6 |
landing in step 7, reached destination |
17 steps taken. |

**Question 15 :**

If Cmn = C(m + n), for what value of n is Cmn neither positive nor negative ?

(A) -C (B) -m (C) 2m (D) 0 (E) 1/m

**Solution :**

We must pick value of n that makes the expression O, since O neither positive nor negative. This occurs when n is the negative of m.

Hence the value of n is -m.

**Question 16 :**

Two sides of a triangle at 6 and 8. What is the length of the third side ?

(A) 2 (B) 4 (C) 5 (D) 10 (E) Cannot be determined

**Solution :**

The sum of length of 2 sides will be greater than the other side. But we could not say the exact length of third side.

Hence, we cannot determine.

**Question 17 :**

2 + (1/3) = 14/b, what is b ?

(A) 3 (B) 6 (C) 7 (D) 9 (E) 28

**Solution :**

2 + (1/3) = 14/b

(6 + 1)/3 = 14/b

7/3 = 14/b

b = 14 (3)/7

b = 6

**Question 19 :**

In the formula V = r^{2}h, if h is doubles and r triples, then V is multiplied by ?

(A) 6 (B) 9 (C) 12 (D) 18 (E) 36

**Solution :**

h = 2h, r = 3r

V = r^{2}h

V = (3r)^{2}(2h)

V = 9r^{2}(2h)

V = 18r^{2}h

**Question 20 :**

Max A returns the largest value in the set A, min A returns the lowest value in the set A. For example, max {1, 2, 3} = 3 and min {0, 4, 5} = 0. What is max {min {x, 2x, 3x}, max{x/2, x/4,x/8}} ?

(A) x (B) 2x (C) x/2 (D) 3x

(E) cannot be determined.

**Solution :**

The answer cannot be uniquely determined, since we do not know if x is negative or positive.

If you would like to have more questions on PSAT math, please click on the links given below.

**PSAT online practice test math - Paper 1**

**PSAT online practice test math - Paper 2**

**PSAT online practice test math - Paper 3**

**PSAT online practice test math - Paper 4**

**PSAT online practice test math - Paper 5**

**PSAT online practice test math - Paper 6**

**PSAT online practice test math - Paper 7**

**PSAT online practice test math - Paper 8**

**PSAT online practice test math - Paper 9**

**PSAT online practice test math - Paper 10**

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