6 questions. Try each one, then open the answer to check yourself and read the explanation.
Make t the subject of the formular s = ut + ½ at²
Answer: D (1/a[−u ± √(u² + 2as)])
Multiply by 2 and rearrange: at² + 2ut − 2s = 0. The quadratic formula gives t = [−2u ± √(4u² + 8as)]/(2a) = (1/a)[−u ± √(u² + 2as)].
If (a²b⁻³c)¾/(a⁻¹b⁴c⁵) = apbqcr. What is the value of P + 2q?
Answer: C (−10)
The left side is a^(3/2 + 1) b^(−9/4 − 4) c^(3/4 − 5), so p = 5/2 and q = −25/4. Then p + 2q = 5/2 − 25/2 = −10.
Solve the equation: m² + n² = 29, m + n = 7?
Answer: B ((2,5) and (5,2))
Put m = 7 − n into m² + n² = 29: n² − 7n + 10 = 0, so n = 2 or 5 and m = 5 or 2.
Make t the subject of formula S = ut + ½at²?
Answer: B (1/a[−u ± √(u² + 2as)])
Rearrange to at² + 2ut − 2S = 0 and use the quadratic formula: t = (1/a)[−u ± √(u² + 2aS)].
What is the obtuse angle formed when the point U is joined to O?
Answer: B (105°)
The construction makes 90° at Q (line QT) and 60° (point S), and U bisects the angle between them, so QU makes 75° with the line on the right. The obtuse angle with QP is 180° − 75° = 105°.
Find the missing point I value in the following road?
x: −2, −1, 0, 1, 2, 3
y = x³ − x + 3: ___, 3, 3, 3, 9, 27
Answer: B (−3)
At x = −2: y = (−2)³ − (−2) + 3 = −8 + 2 + 3 = −3.