Daily Practice · Higher Plus
January 1975 5-a-day
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The batch download puts all 5 tiers' January 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1975A rectangle is 12 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd January 1975f(x) = 7x + 7. Work out the inverse function f^-1(x).
- 3rd January 1975y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 4th January 1975In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 5th January 1975A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th January 1975On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th January 1975Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 8th January 1975Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 9th January 1975y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 10th January 1975A cuboid measures 8 cm by 7 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th January 1975A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th January 1975A 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?
- 13th January 1975A block has mass 270 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th January 1975Use the iteration x(n+1) = cube root of (6x(n) + 8) with x(0) = 4. Work out x(1) to 3 decimal places.
- 15th January 1975y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 16th January 1975A cuboid measures 12 cm by 13 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th January 1975A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th January 1975On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th January 1975x = 149 and y = 98, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th January 1975Work out the nth term of the quadratic sequence -6, -1, 10, 27, ...
- 21st January 1975A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd January 1975The 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.
- 23rd January 1975A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 24th January 1975A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 25th January 1975A car covers 120 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.
- 26th January 1975The point (5, 1) lies on y = f(x). Write down its image on y = f(x + 3).
- 27th January 1975y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 28th January 1975In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 29th January 1975The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 30th January 1975On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st January 1975Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.