Daily Practice · Higher Plus
August 1964 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1964 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1964
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1964A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 2nd August 1964x = 52 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd August 1964Simplify (x^2 - 2x - 3)/(x - 3).
- 4th August 1964y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 49.
- 5th August 1964A cuboid measures 15 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th August 1964A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th August 1964On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th August 1964A car covers 640 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th August 1964In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 8 in terms of an integer n?
- 10th August 1964A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 11th August 1964A cuboid measures 8 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th August 1964A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th August 1964A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 14th August 1964Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 15th August 1964Make x the subject of 2x + 7 = y(x + 7).
- 16th August 1964y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 17th August 1964The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 18th August 1964A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 19th August 1964On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th August 1964Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 21st August 1964Write 7/(x - 2) + 7/(x - 1) as a single fraction.
- 22nd August 1964y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 23rd August 1964In 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.
- 24th August 1964The probability of winning a game is 4/5. A player expects 72 wins. How many games did they play?
- 25th August 1964A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 26th August 1964A rectangle is 11 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th August 1964Solve 4x^2 + 17x + 4 = 0.
- 28th August 1964y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 16.
- 29th August 1964In a vector proof you find that vector PQ = 4a + 6b and vector RS = 12a + 18b. What does this show about PQ and RS?
- 30th August 1964A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 31st August 1964On 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?