Daily Practice · Higher Plus
January 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2007A block has mass 880 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd January 2007Write x^2 + 16x - 2 in the form (x + a)^2 + b.
- 3rd January 2007y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 4th January 2007The 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.
- 5th January 2007A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 6th January 2007On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th January 2007x = 192 and y = 108, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th January 2007Work out the coordinates of the turning point of y = x^2 + 6x + 10.
- 9th January 2007y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 10th January 2007In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 11th January 2007The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 12th January 2007A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 13th January 2007A car covers 860 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th January 2007Simplify (x^2 + 4x - 12)/(x + 6).
- 15th January 2007y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 49.
- 16th January 2007In a vector proof you find that vector PQ = 4a - 4b and vector RS = 16a - 16b. What does this show about PQ and RS?
- 17th January 2007A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 18th January 2007On 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?
- 19th January 2007Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 20th January 2007In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 21st January 2007A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 22nd January 2007A cuboid measures 5 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd January 2007A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th January 2007A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 25th January 2007Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 26th January 2007Make x the subject of 7x + 4 = y(x + 4).
- 27th January 2007y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 28th January 2007A cuboid measures 12 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th January 2007A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th January 2007On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st January 2007A rectangle is 9 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.