Daily Practice · Higher Plus
February 1978 5-a-day
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The batch download puts all 5 tiers' February 1978 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1978A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 2nd February 1978Simplify sqrt(45) + sqrt(80), giving your answer in the form a sqrt(b).
- 3rd February 1978Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 4th February 1978y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 5th February 1978The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 6th February 1978A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 7th February 1978On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th February 1978A rectangle is 20 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th February 1978Use the iteration x(n+1) = cube root of (8x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
- 10th February 1978y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 11th February 1978In 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.
- 12th February 1978The probability of winning a game is 7/8. A player expects 49 wins. How many games did they play?
- 13th February 1978A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 14th February 1978Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 15th February 1978Work out the nth term of the quadratic sequence 2, 4, 8, 14, ...
- 16th February 1978y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 9.
- 17th February 1978In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 18th February 1978A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 19th February 1978On 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?
- 20th February 1978A block has mass 750 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st February 1978The point (2, 0) lies on y = f(x). Write down its image on y = f(x + 2).
- 22nd February 1978A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd February 1978A cuboid measures 12 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th February 1978A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th February 1978A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 26th February 1978x = 41 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th February 1978Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 28th February 1978y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.