Daily Practice · Higher Plus
July 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1984f(x) = 4x + 1. Work out the inverse function f^-1(x).
- 2nd July 1984y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 16.
- 3rd July 1984The 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.
- 4th July 1984A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 5th July 1984On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th July 1984Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 7th July 1984Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 8th July 1984A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 9th July 1984In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 10th July 1984The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 11th July 1984A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 12th July 1984Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 13th July 1984Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 14th July 1984y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 15th July 1984In a vector proof you find that vector PQ = 5a + 3b and vector RS = 10a + 6b. What does this show about PQ and RS?
- 16th July 1984A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 17th July 1984On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th July 1984A rectangle is 29 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th July 1984Work out the nth term of the quadratic sequence -2, 5, 16, 31, ...
- 20th July 1984y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 21st July 1984A cuboid measures 12 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd July 1984A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd July 1984A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 24th July 1984Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 25th July 1984The point (-5, -2) lies on y = f(x). Write down its image on y = -f(x).
- 26th July 1984y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 36.
- 27th July 1984A cuboid measures 7 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th July 1984A bag holds 6 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th July 1984On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th July 1984A block has mass 700 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 31st July 1984Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.