Daily Practice · Higher Plus
January 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1986The probability of winning a game is 7/8. A player expects 14 wins. How many games did they play?
- 2nd January 1986A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 3rd January 1986Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 4th January 1986The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 5th January 1986y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 25.
- 6th January 1986In a vector proof you find that vector PQ = 3a + b and vector RS = 9a + 3b. What does this show about PQ and RS?
- 7th January 1986A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 8th January 1986On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th January 1986Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 10th January 1986A quadratic sequence starts 11, 20, 33, 50. Work out the second difference, and the coefficient of n^2.
- 11th January 1986A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 12th January 1986A cuboid measures 3 cm by 3 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th January 1986A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th January 1986A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 15th January 1986A rectangle is 13 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th January 1986Solve x^2 - x - 12 < 0.
- 17th January 1986y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 18th January 1986A cuboid measures 11 cm by 11 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th January 1986A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th January 1986On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st January 1986Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 22nd January 1986Write x^2 + 4x + 8 in the form (x + a)^2 + b.
- 23rd January 1986y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 24th January 1986The 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.
- 25th January 1986A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 26th January 1986A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 27th January 1986A block has mass 460 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.
- 28th January 1986Work out the coordinates of the turning point of y = x^2 - 8x + 12.
- 29th January 1986y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 36.
- 30th January 1986In 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.
- 31st January 1986The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?