Daily Practice · Higher Plus
June 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1992 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1992f(x) = 3x - 5 and g(x) = 5x + 4. Work out fg(6).
- 2nd June 1992y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 3rd June 1992In a vector proof you find that vector PQ = 3a - 5b and vector RS = 6a - 10b. What does this show about PQ and RS?
- 4th June 1992A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 5th June 1992On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th June 1992A car covers 250 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th June 1992The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 8th June 1992y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 9th June 1992A cuboid measures 7 cm by 4 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th June 1992A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th June 1992A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 12th June 1992Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 13th June 1992A quadratic sequence starts 12, 24, 42, 66. Work out the second difference, and the coefficient of n^2.
- 14th June 1992y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 9.
- 15th June 1992A cuboid measures 12 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th June 1992A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th June 1992On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th June 1992Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 19th June 1992Solve x^2 - 10x + 16 > 0.
- 20th June 1992A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 21st June 1992The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 22nd June 1992A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 23rd June 1992A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 24th June 1992A rectangle is 10 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th June 1992Write x^2 - 16x - 1 in the form (x + a)^2 + b.
- 26th June 1992y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 27th June 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.
- 28th June 1992The probability of winning a game is 1/5. A player expects 15 wins. How many games did they play?
- 29th June 1992On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th June 1992Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).