Daily Practice · Higher Plus
January 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1989y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 2nd January 1989A cuboid measures 13 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd January 1989A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th January 1989On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th January 1989Simplify sqrt(45) + sqrt(245), giving your answer in the form a sqrt(b).
- 6th January 1989Work out the nth term of the quadratic sequence 5, 19, 39, 65, ...
- 7th January 1989y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 8th January 1989The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 9th January 1989A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 10th January 1989A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 11th January 1989A rectangle is 14 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th January 1989The point (-5, 1) lies on y = f(x). Write down its image on y = f(x + 5).
- 13th January 1989y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 9.
- 14th January 1989In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 15th January 1989The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?
- 16th January 1989On 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?
- 17th January 1989Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 18th January 1989Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 19th January 1989A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 20th January 1989In a vector proof you find that vector PQ = 4a + b and vector RS = 12a + 3b. What does this show about PQ and RS?
- 21st January 1989A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 22nd January 1989A 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?
- 23rd January 1989A block has mass 800 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.
- 24th January 1989f(x) = 3x + 1 and g(x) = 6x - 8. Work out fg(-3).
- 25th January 1989y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 26th January 1989A cuboid measures 7 cm by 10 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th January 1989A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th January 1989On 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?
- 29th January 1989x = 118 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th January 1989The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 31st January 1989y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.