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Mixed skills
10 original practice questions · Untimed · Fractions and exact decimals accepted
1. Two angles in a triangle measure 34° and 48°. What is the third angle in degrees?
psat-triangles-1-12. A cafeteria sold 12 lunches, each either soup or pasta. Pasta lunches numbered twice the soup lunches. How many pasta lunches were sold?
psat-systems-1-13. A vehicle averages 25 miles per US gallon. Use 1 mile=8/5 kilometers and 1 US gallon=19/5 liters. How many liters does the model use per 100 kilometers?
psat-compound-units-4-24. The function q(x) = (x − 4)(x + 6) has two zeros. What is their distance on the number line?
psat-quadratic-1-15. A constant function g has g(5) = 11. What is g(7)?
psat-relationships-4-26. A tank starts with 70 liters and drains 7 liters per minute at a constant rate. How many liters remain after 4 minutes?
psat-linear-4-47. A rectangular garden is 2 meters longer than it is wide and has area 24 square meters. What is its perimeter in meters?
psat-quadratic-4-18. Population A contains 5,7; population B contains 3,9. What is B’s population standard deviation divided by A’s?
psat-spread-and-frequency-2-39. The equations 4x + 2y = 10 and 8x + 4y = c represent the same line. What is c?
psat-systems-4-110. The function h(x) = 2(x − 6)² + 8 has a minimum. At what x-value does the minimum occur?
psat-quadratic-2-3Answers & reasoning
1. 98 · Choice A
The three interior angles sum to 180 degrees. Subtract both known angles from that total. The requested value is 98.
psat-triangles-1-12. 8 · Choice C
Represent soup by s and pasta by 2s. Their total is 3s, so find one part and multiply by two. The requested value is 8.
psat-systems-1-13. 19/2 · Choice B
Convert the distance per gallon into kilometers per gallon. Divide 100 kilometers by that distance, then multiply the resulting gallons by liters per gallon. Substitute the given numbers: 100 × (19 ÷ 5) ÷ (25 × (8 ÷ 5)) = 19/2. The requested value is 19/2.
psat-compound-units-4-24. 10 · Choice D
Set each factor equal to zero to obtain the two roots. Subtract the negative root from the positive root to get their distance. The requested value is 10.
psat-quadratic-1-15. 11 · Choice A
A constant function has zero rate of change. The output is unchanged when the input changes. The requested value is 11.
psat-relationships-4-26. 42 · Choice C
Find the total removed in four minutes. Subtract the removed volume from the starting volume. The requested value is 42.
psat-linear-4-47. 20 · Choice B
A positive width w must satisfy w(w+2) equal to the area. Find the positive width, then add both lengths and both widths. The requested value is 20.
psat-quadratic-4-18. 3 · Choice C
Both population means are 6. A has deviations of magnitude 1, B of magnitude 3. For each symmetric pair, the population standard deviation equals that deviation magnitude. SD(A)=√((1²+1²)/2)=1; SD(B)=√((3²+3²)/2)=3; ratio=3÷1=3. The requested value is 3.
psat-spread-and-frequency-2-39. 20 · Choice B
The left side of the second equation is twice the first. For identical solution sets, the right side must also be doubled. The requested value is 20.
psat-systems-4-110. 6 · Choice D
A square is nonnegative, and multiplying by two preserves that. The minimum occurs when the squared expression is zero. The requested value is 6.
psat-quadratic-2-3Original parameterized practice, independently checked by computation. Educator review pending. Not an official exam paper.