Math Diagnostic Assessment

Grade 12 | 10 Questions | 20 Minutes

Instructions

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Student Information

Math Diagnostic Test - Grade 12 ⏰ Time Remaining: 20:00
1 2 3 4 5 6 7 8 9 10
Question 1 / 10
Limits Easy
What is lim(x→3) of (x² - 9)/(x - 3)?
0 1 2 3 4 5 0 2 4 6 8 f(x) = (x² - 9)/(x - 3)
Question 2 / 10
Derivatives Easy
Find the derivative of f(x) = x³
x y f(x) = x³ tangent Power Rule: d/dx(x^n) = nx^(n-1) -1 1 2
Question 3 / 10
Integration Easy
What is ∫ 2x dx?
0 1 2 3 4 5 0 2 4 6 8 10 y = 2x Area = ∫2x dx Integration: ∫nx dx = (n/2)x² + C
Question 4 / 10
Trigonometry Medium
What is sin(π/2)?
x y (1, 0) (0, 1) (-1, 0) (0, -1) π/2 1 Unit Circle: sin(θ) = y-coordinate 90° = π/2
Question 5 / 10
Exponential Functions Medium
Solve for x: e^x = e³
0 1 2 3 4 0 e e² e³ y = e^x If e^x = e^a, then x = a
Question 6 / 10
Logarithms Medium
Simplify: log₂(8)
0 1 2 4 8 x 0 1 2 3 4 y = log₂(x) (8, 3) log₂(8) = 3 because 2³ = 8
Question 7 / 10
Polynomial Medium
Find the zeros of f(x) = x² - 5x + 6
0 1 2 3 4 5 6 0 2 4 6 x=2 x=3 vertex f(x) f(x) = x² - 5x + 6
Question 8 / 10
Sequences Hard
What is the sum of arithmetic series: 2 + 5 + 8 + ... + 29? (a₁=2, d=3, aₙ=29)
2 + 5 + 8 + ... + 29 +3 +3 Sum = (n/2)(a₁ + aₙ) n = number of terms = 10 Sum = (10/2)(2 + 29) = 5 × 31 = ? Arithmetic Series: a₁=2, d=3, n=10
Question 9 / 10
Probability Hard
How many ways can you arrange 4 books on a shelf? (4! = 4 × 3 × 2 × 1)
A B C D Permutations: n! arrangements Position 1: 4 choices Position 2: 3 choices × Position 3: 2 choices × Position 4: 1 choice 4! = 4 × 3 × 2 × 1 = ? 1st 2nd 3rd 4th
Question 10 / 10
Matrices Hard
What is the determinant of [[2, 3], [1, 4]]? (det = ad - bc)
2 3 1 4 a b c d det = ad - bc = (2)(4) - (3)(1) = 8 - 3 = ? 2×2 Matrix Determinant Main diagonal (ad): 2 × 4 = 8 Anti-diagonal (bc): 3 × 1 = 3 Determinant = 8 - 3 = ?
Question 1 of 10

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