Daily Practice · Higher Plus
May 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1992Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 2nd May 1992Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 3rd May 1992A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 4th May 1992In a vector proof you find that vector PQ = a - 3b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 5th May 1992A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th May 1992A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 7th May 1992Simplify sqrt(75) + sqrt(147), giving your answer in the form a sqrt(b).
- 8th May 1992Use the iteration x(n+1) = cube root of (5x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 9th May 1992y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 10th May 1992A cuboid measures 7 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th May 1992A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th May 1992On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th May 1992A rectangle is 29 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th May 1992Work out the nth term of the quadratic sequence 6, 7, 10, 15, ...
- 15th May 1992y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 16th May 1992A cuboid measures 12 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th May 1992A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th May 1992A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 19th May 1992Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 20th May 1992The point (1, -2) lies on y = f(x). Write down its image on y = f(x + 5).
- 21st May 1992y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 36.
- 22nd May 1992The 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.
- 23rd May 1992A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 24th May 1992On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th May 1992A block has mass 890 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th May 1992Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 27th May 1992A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 28th May 1992In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 29th May 1992The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 30th May 1992A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 31st May 1992x = 33 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.