Daily Practice · Higher Plus
July 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1991Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 2nd July 1991y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 3rd July 1991In 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.
- 4th July 1991The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 5th July 1991On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th July 1991A car covers 760 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.
- 7th July 1991Use the iteration x(n+1) = cube root of (12x(n) + 6) with x(0) = 5. Work out x(1) to 3 decimal places.
- 8th July 1991y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 9th July 1991In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 10th July 1991A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 11th July 1991A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 12th July 1991Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 13th July 1991Work out the nth term of the quadratic sequence 2, 10, 24, 44, ...
- 14th July 1991y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 64.
- 15th July 1991A cuboid measures 3 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th July 1991A 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?
- 17th July 1991On 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 July 1991Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 19th July 1991The point (0, 0) lies on y = f(x). Write down its image on y = f(x + 2).
- 20th July 1991A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 21st July 1991A cuboid measures 9 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd July 1991A 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?
- 23rd July 1991A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 24th July 1991A rectangle is 12 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th July 1991Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 26th July 1991y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 27th July 1991The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 28th July 1991A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 29th July 1991On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th July 1991Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 31st July 1991f(x) = 6x - 7 and g(x) = 3x - 6. Work out fg(-2).