Question 1
Differentiate y = 5 cos(3x + 4)
Hint
Keep the angle unchanged and include the inner multiplier.
Higher Mathematics
Higher Maths Readiness Check
A pupil-facing snapshot of National 5 foundations and early Higher Mathematics skills. Equivalent exact answers are accepted; the result is intended to identify strengths, gaps and useful next steps.
Readiness snapshot
Check key skills
Answer each question, then check it. When all questions are checked, your readiness result and suggested next practice will appear.
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Differentiation
Question 2
For uₙ₊₁ = ₙ + 5, find the limiting value if it converges.
Hint
Replace both uₙ₊₁ and uₙ with L.
Question 3
A(-1, −2), B(3, −4) and C(11, −8). Show that A, B and C are collinear.
Hint
Find two vectors from the same starting point and compare them as scalar multiples.
Question 4
Solve x² − 6x = 0.
Hint
Find two numbers that multiply to c and add to b.
Question 5
State the multiplier for decay of 20% per time period.
Hint
Growth multipliers are above 1; decay multipliers are below 1.
Question 6
Find the midpoint of (-7, −7) and (3, −1).
Hint
Add each coordinate pair, then divide by 2.
Question 7
Given tan x = and x is acute, find cos 2x exactly
Hint
Use a double-angle identity written in terms of tangent.
Question 8
Find the normal to y = x² at x = 1.
Hint
Use the negative reciprocal for the normal gradient.
Question 9
The curve y = x² is listed before the line y = 5x. Find the enclosed area.
Hint
Choose top minus bottom from the graph or a test value, not from the order named.
Question 10
Describe the transformation from y = f(x) to y = f(x) + 4
Hint
Outside the function means vertical movement.