explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"ded7b098-d02b-4ee9-a5a8-173e380231cb","revisionId":"73d37858-7534-4fea-8728-180e1977a840","questionNumber":null,"questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"8349b189-b857-4cc8-8736-bf82f17d4ff4","label":"a","content":"Find the gradient of the line that passes through $(3, 8)$ and $(5, 2)$.","markscheme":"- Uses $m = \\frac{2 - 8}{5 - 3}$ M1\n- $\\frac{-6}{2} = -3$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of using the gradient formula $\\frac{y_2 - y_1}{x_2 - x_1}$ with coordinates correctly substituted.","code":"M"},{"id":"p2","marks":1,"description":"Correct calculation resulting in -3.","code":"A"}],"finalAnswers":["-3"],"generatedAt":"2026-05-06T14:06:03.219Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"gradient_formula","label":"Use the gradient formula","steps":[{"type":"text","order":0,"title":"Recall the formula","content":"For two points, the gradient is the change in $y$ divided by the change in $x$:\n\n$$m=\\frac{y_2-y_1}{x_2-x_1}$$\n\nKeep the coordinates in the same order in the numerator and denominator.","highlights":[{"text":"Find the gradient of the line","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$m=\\dfrac{\\htmlData{anchor=y_formula}{\\color{@sky}{y_2-y_1}}}{\\htmlData{anchor=x_formula}{\\color{@orange}{x_2-x_1}}}$"},{"latex":"$$m=\\dfrac{\\htmlData{anchor=y_values}{\\color{@sky}{2-8}}}{\\htmlData{anchor=x_values}{\\color{@orange}{5-3}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"y_values"},{"color":"orange","style":"text-color","anchor":"x_values"}],"connections":[{"to":"y_values","from":"y_formula","color":"sky","label":"substitute y-values"}]},"order":1,"title":"Substitute the coordinates","description":"Use the first point for the first pair of values and the second point for the second pair. Substitute the y-values in the numerator and the x-values in the denominator. This correct substitution earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$m=\\frac{\\color{@purple}{\\htmlData{anchor=changes}{2-8}}}{\\color{@purple}{5-3}}$"},{"latex":"$$m=\\frac{\\color{@teal}{\\htmlData{anchor=fraction}{-6}}}{\\color{@teal}{2}}$"},{"latex":"$$m=\\color{@green}{\\htmlData{anchor=result}{-3}}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"changes"},{"color":"teal","style":"text-color","anchor":"fraction"},{"color":"green","style":"text-color","anchor":"result"}],"connections":[{"to":"fraction","from":"changes","color":"purple","label":"work out differences"}]},"order":2,"title":"Calculate the gradient","description":"Work out the vertical and horizontal changes. Then divide −6 by 2 to get −3. The negative answer means the line slopes downwards from left to right; the correct value earns the A1 mark."}]}],"generatedAt":"2026-07-19T07:43:53.266Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"eadccd3d-2519-4e97-b34b-27f16ae6db34","revisionId":"e4555bca-613d-4cc7-8151-af417b98216a","questionNumber":null,"questionType":"LA","specification":"The line $PQ$ passes through the points $P(-2, 3)$ and $Q(4, k)$.\n\nThe gradient of $PQ$ is $1.5$.","difficulty":3,"difficultyBand":"hard","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"b94f5812-51f8-4bec-acf9-abf055233e57","label":"a","content":"Work out the value of $k$.","markscheme":"- Sets up equation $1.5 = \\frac{k - 3}{4 - (-2)}$ M1\n- Simplifies to $1.5 = \\frac{k - 3}{6}$ and multiplies by 6 to get $9 = k - 3$ M1\n- $k = 12$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Sets up the gradient equation usi

Gradient of a Line Questions

Gradient of a Line Questions

Gradient of a Line Questions

Gradient of a Line Questions