Bluebook SAT Test Digital SAT Hard Math 2

Question 1

The sum of three consecutive even integers is 78. What is the largest of the three integers?

Accepted Answer

28

Answer

Let the integers be n, n+2, n+4. Then 3n+6 = 78, so n = 24. The largest is n+4 = 28.

Question 2

If x² - y² = 24 and x - y = 4, what is the value of x + y?

Accepted Answer

6

Answer

(x-y)(x+y) = 24. Since x-y = 4, we get 4(x+y) = 24, so x+y = 6.

Question 3

A line passes through points (a, 3) and (4, a+1) and has a slope of 2. What is the value of a?

Accepted Answer

1

Answer

Slope = (a+1-3)/(4-a) = (a-2)/(4-a) = 2. So a-2 = 2(4-a) = 8-2a, giving 3a = 10... wait: a-2=8-2a → 3a=10 → no. Let me recheck: a=1 gives slope (2-2)/(3)... Actually: slope = (a+1-3)/(4-a) = 2 → a-2=8-2a → 3a=10 → a=10/3. Re-examining answer: if slope=2, (a-2)/(4-a)=2, a-2=8-2a, 3a=10, which gives a non-integer. Trying a=1: (0)/3=0 ≠ 2. The correct setup with given answer a=1 requires re-reading. With slope=(a+1-3)/(4-a)=2: a-2=2(4-a); a-2=8-2a; 3a=10; a=10/3. So a=1 doesn't work — the correct answer should be interpreted differently.

Question 4

The graph of y = ax² + bx + c has vertex at (2, -5) and passes through (0, 3). What is the value of a?

Accepted Answer

2

Answer

Vertex form: y = a(x-2)² - 5. At (0,3): 3 = a(4) - 5, so 4a = 8, a = 2.

Question 5

If (x - 2)(x + 5) = x² + kx - 10, what is the value of k?

Accepted Answer

3

Answer

Expanding: x² + 5x - 2x - 10 = x² + 3x - 10. So k = 3.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Bluebook SAT Test Digital SAT Hard Math 2