Daily Practice · Higher Plus
September 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1993 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1993y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 2nd September 1993A cuboid measures 10 cm by 12 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd September 1993A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th September 1993On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th September 1993x = 110 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th September 1993Write 2/(x + 6) + 2/(x - 6) as a single fraction.
- 7th September 1993y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 8th September 1993A cuboid measures 11 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th September 1993A bag holds 5 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th September 1993A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 11th September 1993A car covers 900 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th September 1993Solve 16x^2 - 8x - 3 = 0.
- 13th September 1993y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
- 14th September 1993The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 15th September 1993A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 16th September 1993On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th September 1993Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 18th September 1993f(x) = 4x - 8. Work out the inverse function f^-1(x).
- 19th September 1993A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 20th September 1993In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 21st September 1993The probability of winning a game is 2/5. A player expects 8 wins. How many games did they play?
- 22nd September 1993A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 23rd September 1993Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 24th September 1993Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 25th September 1993y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 26th September 1993In a vector proof you find that vector PQ = 2a - 6b and vector RS = 8a - 24b. What does this show about PQ and RS?
- 27th September 1993A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 28th September 1993On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th September 1993A rectangle is 6 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th September 1993Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.