Daily Practice · Higher Plus
August 1968 5-a-day
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The batch download puts all 5 tiers' August 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1968y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 2nd August 1968In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 3rd August 1968The probability of winning a game is 1/2. A player expects 65 wins. How many games did they play?
- 4th August 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 5th August 1968A block has mass 210 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th August 1968Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 7th August 1968y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 8th August 1968In a vector proof you find that vector PQ = 6a + b and vector RS = 12a + 2b. What does this show about PQ and RS?
- 9th August 1968A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 10th August 1968On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th August 1968x = 57 and y = 30, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th August 1968Use the iteration x(n+1) = cube root of (11x(n) + 6) with x(0) = 1. Work out x(1) to 3 decimal places.
- 13th August 1968A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 14th August 1968A cuboid measures 9 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th August 1968A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th August 1968A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 17th August 1968A car covers 670 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th August 1968Work out the nth term of the quadratic sequence -4, -3, 2, 11, ...
- 19th August 1968y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 20th August 1968A cuboid measures 14 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st August 1968A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd August 1968On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd August 1968Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 24th August 1968The point (-6, 0) lies on y = f(x). Write down its image on y = f(-x).
- 25th August 1968y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 26th August 1968The 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.
- 27th August 1968A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 28th August 1968A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 29th August 1968Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 30th August 1968Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 31st August 1968y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.