Daily Practice · Higher Plus
June 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1993 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1993Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 2nd June 1993Solve 8x^2 - 10x - 3 = 0.
- 3rd June 1993y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 4th June 1993A cuboid measures 7 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th June 1993A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th June 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 7th June 1993A block has mass 440 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th June 1993f(x) = 5x + 3. Work out the inverse function f^-1(x).
- 9th June 1993y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 64.
- 10th June 1993A cuboid measures 13 cm by 11 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th June 1993A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th June 1993On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th June 1993x = 91 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th June 1993Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 15th June 1993A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 16th June 1993The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 17th June 1993A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 18th June 1993A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 19th June 1993A car covers 710 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th June 1993Use the iteration x(n+1) = cube root of (4x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 21st June 1993y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 22nd June 1993In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 23rd June 1993The probability of winning a game is 2/5. A player expects 8 wins. How many games did they play?
- 24th June 1993On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th June 1993Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 26th June 1993Work out the nth term of the quadratic sequence 9, 20, 37, 60, ...
- 27th June 1993y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 28th June 1993In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
- 29th June 1993A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 30th June 1993A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?