Daily Practice · Higher Plus
February 1985 5-a-day
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The batch download puts all 5 tiers' February 1985 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1985Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 2nd February 1985Use the iteration x(n+1) = cube root of (9x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
- 3rd February 1985y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 36.
- 4th February 1985In 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.
- 5th February 1985The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
- 6th February 1985On 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?
- 7th February 1985Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 8th February 1985Work out the nth term of the quadratic sequence 1, 7, 15, 25, ...
- 9th February 1985A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
- 10th February 1985In a vector proof you find that vector PQ = 4a + 3b and vector RS = 20a + 15b. What does this show about PQ and RS?
- 11th February 1985A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 12th February 1985A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 13th February 1985A rectangle is 19 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th February 1985The point (4, -4) lies on y = f(x). Write down its image on y = f(x + 3).
- 15th February 1985y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 16th February 1985A cuboid measures 13 cm by 12 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th February 1985A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th February 1985On 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?
- 19th February 1985Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
- 20th February 1985Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 21st February 1985y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 22nd February 1985A cuboid measures 9 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd February 1985A bag holds 5 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th February 1985A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 25th February 1985A block has mass 550 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th February 1985f(x) = 4x - 1 and g(x) = 3x - 1. Work out fg(3).
- 27th February 1985y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 25.
- 28th February 1985The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.