Daily Practice · Higher Plus
January 1968 5-a-day
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The batch download puts all 5 tiers' January 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1968A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 2nd January 1968Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 3rd January 1968Solve 4x^2 - 12x + 5 = 0.
- 4th January 1968y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 36.
- 5th January 1968In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 6th January 1968The probability of winning a game is 3/10. A player expects 12 wins. How many games did they play?
- 7th January 1968On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th January 1968A block has mass 870 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th January 1968f(x) = 5x - 1. Work out the inverse function f^-1(x).
- 10th January 1968A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 11th January 1968In a vector proof you find that vector PQ = 5a + b and vector RS = 15a + 3b. What does this show about PQ and RS?
- 12th January 1968A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 13th January 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 14th January 1968x = 199 and y = 124, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th January 1968Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 16th January 1968y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 17th January 1968A cuboid measures 5 cm by 3 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th January 1968A 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?
- 19th January 1968On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th January 1968A car covers 770 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st January 1968Use the iteration x(n+1) = cube root of (2x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 22nd January 1968y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 23rd January 1968A cuboid measures 5 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th January 1968A bag holds 5 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th January 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 26th January 1968Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 27th January 1968Work out the nth term of the quadratic sequence -1, 2, 9, 20, ...
- 28th January 1968y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 29th January 1968The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 30th January 1968A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 31st January 1968On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?